Symmetric Powers of Galois Modules on Dedekind Schemes

We prove a certain Riemann–Roch-type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou–Noguès–Taylor operations.     

Chemical Composition and Microstructure of Plasma-Nitrided Aluminium

 Detailed examinations were made by AES depth profiling, SEM, TEM and electron diffraction to get information about the relation between treatment conditions and the state of plasma-nitrided aluminium. The chemical composition and the elemental depth distribution were proofed to be depending on gas phase mixture, pressure and temperature during plasma treatment. The admixture of hydrogen during presputtering for surface cleaning and during nitriding results both in an improved nitriding behaviour and in a reduction of the formation of conical-shaped particles at the surface. The microstructure of the nitride layer isn’t depending on tested process conditions significantly. Surface and interface between layer and substrate are roughly in a scale of a few ten nanometers owing to sputtering effects. The main phase inside the layer is nanocrystalline AlN of the known hexagonal modification. In addition, some crystallites of remaining aluminium are present as a second phase. In contrast to nitrogen-implanted aluminium no preferred lattice orientation of the AlN phase was evident.     

A New Kinetic Model for Water Sorption Isotherms of Cellulosic Materials

Summary: Some natural fibres like flax, hemp and others show excellent mechanical properties which make them a promising choice for the reinforcement of polymers. For natural fibre reinforced composites, hydrophilicity is a problem with respect to dimensional changes, fibre to matrix adhesion and long term stability. The interaction of differently prepared and modified fibres with water vapour has been investigated by dynamic vapour sorption. It has been found that the sorption and desorption kinetics of cellulosic fibres can be excellently fitted by assuming two parallel, independent first order processes. This empirical model, defined here as the “Parallel Exponential Kinetics” model (PEK-model), reveals two distinct mechanisms with slow and fast exchange of water vapour respectively, related to different sorption sites. The specific sorption mechanisms are represented by individual sorption-desorption isotherms as components of the total isotherms. The results suggest a relation to the differing types of amorphous regions in the fibres and/or to the different states of “bound” or “free” water, discussed for hydrophilic materials. The PEK-model proved to be consistently applicable for sorption and desorption over the whole humidity range, and also for all tested cellulose fibres. It is especially useful for a clearer distinction of different fibre types or modifications and can be successfully used for an extended fibre characterization.     

On Kato’s Method for Navier–Stokes Equations

We investigate Kato’s method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier–Stokes equations, our approach unifies several results known in the literature, partly with different proofs. Moreover, we establish new existence and uniqueness results for rough initial data on arbitrary domains in \mathbbR³{\mathbb{R}}^{3} and irregular domains in \mathbbRⁿ{\mathbb{R}}^{n}.     

A novel class of thermodynamically consistent isotropic hardening rules for some damage models at finite strains

This paper proposes isotropic hardening rules for plasticity damage models which satisfy the 2nd law of thermodynamics. Here, the Gurson -model modified by Tvergaard/Needleman is used as a prototype model for finite strains to discuss main properties of the novel hardening rules. Additionally it is shown that thermodynamically consistent rules are suitable to fit experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of cementitious materials exposed to isothermal calcium leaching,considering process kinetics and advective water flow. Part 2: Numerical solution

The second part of the paper presents numerical solutions of the mathematical model of hydro-chemo-mechanical behavior of cementitious materials exposed to contact with deionized water of part 1. The model defines kinetics of the calcium leaching process instead of a direct application of a curve describing equilibrium between solid calcium in the material skeleton and the calcium dissolved in the pore solution. It further takes into account the advective flux of calcium ions. Both aspects are new as compared to previous models. The weak form of the governing equations of the model is derived first using the Galerkin method. Then, the equations are discretized in space with finite elements and in time domain with finite differences, and finally the procedures used for numerical solution of their discretized form are presented. Three numerical examples are solved to test the numerical solution procedure proposed and demonstrate its robustness for solution of 1D and 2D problems concerning fast and slow leaching of cement-based materials. The effect of various factors on the results concerning chemical degradation of structures made of cementitious materials is analyzed as well.     

Ultrahigh molecular weight alternating propene/ethene/carbon monoxide terpolymers with elastic properties

Soluble propene/ethene/CO terpolymers (EPEC) with ultrahigh molecular weight (up to 1.2 × 10⁶ g/mol) were prepared by the use of dicationic palladium(II) phosphine catalysts and an optimized amount of water as activator. When the molar ratio of ethene/CO to propene/CO is below 50 mol-%, the terpolymers are thermoplastic elastomers with excellent properties. Above this ratio the terpolymers are crystalline thermoplastics. The ultrahigh molecular weight elastomers are highly soluble in organic solvents such as CH₂Cl₂ and CHCl₃.